Question

1) A cone and cylinder stand on same base and have the same height then ratio of their volumes will be:


(a) 1 : 1

(b) 1 : 3

(c) 3 : 1

(d) 1 : 2​

Answer 1

Answer:

Given.

A cone, a hemisphere, and a cylinder stand on equal bases.

Hence radius of base of cone = radius of hemisphere = radius of cylinder=r

And,

They also have same height =h

Hight of cone =h

Hight of cylinder=h

Hight of Hemisphere r=h (r is the radius of sphere)

Now,

Volume of cone V

C

=

3

1

πr

2

h...….(1)

Volume of hemisphere V

H

=

3

2

πr

2

×r

=

3

2

πr

2

×h

V

H

=

3

2

πr

2

h…….(2)

Volume of cylinder V

c

=πr

2

h...…..(3)

From equation 1,2 and 3

V

C

:V

H

:V

c

=

3

1

πr

2

h:

3

2

πr

2

h:πr

2

h

V

C

:V

H

:V

c

=

3

1

:

3

2

:1

V

C

:V

H

:V

c

=1:2:3

Answer 2

Answer:

The correct answer is (b) 1:3.